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The Department of Foreign Languages of a liberal arts college conducted a survey of its recent...

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Advance Math

The Department of Foreign Languages of a liberal arts collegeconducted a survey of its recent graduates to determine the foreignlanguage courses they had taken while undergraduates at thecollege. Of the 550 graduates 207 had at least one year of Spanish.174 had at least one year of French. 143 had at least one year ofGerman. 34 had at least one year of Spanish and French. 26 had atleast one year of Spanish and German. 22 had at least one year ofFrench and German. 3 had at least one year of all threelanguages.

(a) How many of the graduates had at least 1 yr of at least oneof the three languages?
  

(b) How many of the graduates had at least 1 yr of exactly one ofthe three languages?


(c) How many of the graduates had less than 1 yr of any of thethree languages?
  

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